Impedance element



March l0, 1931. w. P. MASON IMPEDANCEELEMENT Filed Sept. 22, 1927 /NvE/vmf? ifi/1mm /P/l/Aso/v 5y/ M rron/vfr Patented Mar. 10, V1931 UNITED STATES PATENT OFFICE WAREN P. IABON, 0I EAST ORANGE, NEW JERSEY, ABSIGNOB- TOBELL TELEPHONE LABORATORIES, INOORPORATED, 0l' NEW YORK, N. Y., .A CORPORATION 0F NIW YORK 'LMPEDANCE ELEMENT Application led September 22, 1927. Serial No. 221,261.

This invention relates to the construction of impedance elements, and more particular- 1y of acoustic impedance elements having impedance of an energy dissipative, or resistive character. An object of vthe invention is to secure a uniform rate of dissipation of energy, or uniform resistance, for a Wide range of Wave frequencies, such as is encountered in `the transmission of speech or music.V

Another object is to secure compactness of structure and economy of material in the construction of acoustic impedance elements. A further object is to facilitate the design and construction of acoustic resistances in accordance with preassigned resistance values.

The term impedance is here used in a general sense to define the ratio of the effective value of a sinusoidally varying force impressed upon a medium to the effective value of the resulting velocity in the medium. ln electrical systems impedance is familiarly defined as the ratio of a sinusoidal E. M. F. to the resulting current, and in mechanical systems it is the ratio of a sinusoidal mechanical force to the resulting vibrational velocity. In acoustic systems the medium by which Waves are transmitted consists of a' gas, generally air at normal atmospheric pressure, and the force by which the wave motion is set up is a pressure variation superimposed upon the normal pressure of the medium. The resulting velocity may be taken as the linear Velocity of the gas particles that is superimposed on their normal random motion, but it is more convenient to define the velocity as the volumetric rate of flow through a given cross sectional surface of the acoustical system. In dealing with systems of the usual type in which the Wave motion is guided by the Walls of a conduit, the term acoustic impedance is used to define the ratio of the excess pressure intensity to the volumetric rate of flow, or volumetric velocity, across a given section of the conduit. The volumetric velocity may or may not be in phase with the excess pressure, and accordingly, if the familiar complex notation Ais used. the impedance will in general be a complex quantity, lYhcf the relocitj.' in

phase with the pressure the impedance has a real value and is said to be resistive.

One method commonly used to obtain resistance in an acoustic system is by the use of screens or plugs of porous material such as hair, felt or cotton, or by the use of mechanical screens having a multiplicity of finely divided passages. When structures like these are used the fiow of air is controlled mainly by viscosity, and the rate of energy dissipation is dependent principally u n the viscosity coefficient of the medium. ethods involving the use of orous structures are better adapted for obtaining high resistances, but on account of the irr ularity of the air passages,d and their small imensions, the resistance values are not readily determined, and are generally quite variable with respect to frequency. Y

Acoustic systems, such as speaking tubes, Wave filters, phonograph horns, and the like, are as a rule provided with conduits of substantial size to prevent the loss of energy due to viscosity. The impedances of acoustic systems are, in consequence, relatively low, and resistance elements for use in connection therewith are most frequently required to be of a correspondingl low value. To obtain acoustic resistance o low value and negligible reactance is a problem of greater difficulty, which heretofore has required the use of structures of inconveniently large dimensions, for example, large diameter tubes of very great length. As is Well known, a uniform air conduit has wave transmission properties resembling those of a section of uniform electrical transmission line. If it is made increasingly long so that wave reflection from the remote end becomes unimportant, the acoustic impedance like the impedance of a uniform electrical line, approaches closely to a constant real value. The constant value of the impedance depends on the elastic and mass coeflicients of the air, and is known as the characteristic acoustic impedance. The impedance of a finite tube, due to wave reflection, or resonance. oscillates with frequency about the characteristic impedance value, but, due to the absorption of energy by viscosity, the reunie ci' the variation decreases graduresistance elements .are constructed yby combining in parallel a 'number of small diameter tubes of progressively varying lengths. The impedance of each tubular element is characterized by periodic variations with fre.

quency, just as in lthe case of a single long I tube, but thel fluctuations in the different tubes occur at different frequencies and mutually compensateeach other. The result of this is that a high degree of uniformity is obtained at all 'frequencies down to a very low value.

For an impedance of equal value and an equal degree of uniformity to that of a given long tube the 'multiple tube structurev of thefin# vention requires only a small'fiaction of the amount of material used in the single tube,

and occupies only a very sinall'fraction of the space. The iii'ipedance'of the combination moreover is susceptible of precise computation from the` dimensions of the device, since it depends almost entirely upon the readily ascertainable coeficiente of mass and elasticity of air.

A particular feature ofthe invention by which the saving of material and space is sub# stantiall increased reIatestothe construction of t e'tubular elements of the combination. According to this feature the elements each comprise a pair of equal tubes one open at its remote end 'and the other closed. vBy this means the length of each tubular element is effectively doubled.

Another feature relates to means for varying the effective resistance of the combination so that a single resistance device may be .i used under different operating conditions.

" transmission system.

. These and other features of the invention 'will be more clearl understood from the .following detailed escription and the accompanying drawings, of which g Fig. 1 shows an acoustic resistance device in accordance with the invention;

Fig. 2 is an end view ofthe device of Fig. 1 illustrating `features of the tube arrangement;

Fig. 3 shows a tubular element embodying a v feature of the invention;

Fig. 4 is an enlarged detail illustrating a preferred embodiment of the invention; and

Fig. 5 illustrates the application of the in-l -vention in connection with an acoustic vwave Referring to Fig. 1, the device there illustrated comprises a group of tubular elementsv l1 of progressively increasing lengths, which,

indicated by Fig 2 which shows an end view 1;?95374 -A i -v tional clamping rings may be used for bind ying thel tubes together atv other points, or

other suitable methods. may be used. The

tubes, all of which are open at the mouth end, ma be either open or closed at their remote en s, .or they may be .grouped in pairs of equal length, each pair comprising an o en and a closed tube. In the 'gui-e the tu es are arranged in the last mentioned manner, as

of the device of g. 1 as seen from above. A longitudinal section lof a paired tubular element is shown Fig. 3.

For the purpose of adapting the device to any particular acoustic system, a tapered connecting tube 3 is provided, which is clamped to the mouth of the device by the screwed couplingv ring 7 The connecting tube 3 should preferably have an exponential taper, and further, should taper very slowly in order that it may be able to transmit freely waves of the lowest speech frequencies. It is advantageous to. construct the tube -Ain several sections as shown, one or more of which may-be removed as desired. This permits the device to'be used in connection with acoustic conduits of different sizes, and at the same time provides means for varying the effective value of the resistance of the device.

The acoustic properties of the structure ion 'willi be understood from the following dis-V cussion of the theoretical principles involved.

The characteristic impedance of a uniform tube, which is the value about which the actual impedance oscillates, is defined as the impedance of an infinitely great length of the tube. In other words the characteristic impedance of a tube is the value of the impedance when the effects ofwave reiiection at the ends are nulliied. Its value, denoted by Zk, for a tube of cross sectional area S is given accurately by the following formula Potthenorinal pressure intensity in the me- 'Y dium, n=the coefficient of viscosity, p=the density,

the 'perimeter of the tube, w=21r times the wave frequency, y=ratio of specific heats.

formula "f5 the tube is closed, and, second when the end' 5` the factor d P o'YP 9 which is'the value of the characteristic imlo pedance when there is no energy dissipatiom The term represents the fractional 'change due to the presence of dissipation.

The vwave propagation constant for unit length of the infinite line is given by the in which the propagation constant is denoted 20 by P, and in which c denotes the velocit of 5 tube. This part is termed the attenuation constant. The imaginarf)r part measures the chan in hase as the wave traverses the tube, an is ca l'ed the phase constant.

The actual im edance of a finite tube of i so length L, depen s not only upon the characteristic impedance but on the reflection eiects due to the manner in which the tube i The first term 4on the right hand side of is terminated. Only two types of termination need be considered, rst when the end of is open. The impedance, Ze, of a closed tube is given by the equation Y zsz, =z coul PL, (ai

and the impedance, Z0, of an open tube is zPL z=z. q =z. mh PL. (4)

The factors within the brackets take account of the reflections at the end of the tubes. As the frequency varies the impedance, Zo or ZC, oscillates between maximum values Zk coth aL, and minima Z.. tanh aL. For an open tube the maxima occur at frequencies pro ortional to the numbers 1, 3, 5, etc., the rst maximum occurring at the frequency for which the length of the tube is a quarter wave length. The minima occur at frequencies pro ortional to the numbers 2, 4, 6, etc. For a c osed tube the frequencies of maximum and minimum impedance are interChanged. At high frequencies the values of tanh L and tory system having an infinite number of resonance and anti-resonance frequencies following each other in alternation at regular coth L both converge to unity and hence thev intervals. The high impedances occur at the anti-resonance points and the' low impedances at the resonance points.

The impedance of a combination of a number of tubes in parallel may be computed by tubes, as expressed by E uations 3 or 4, in the mannerappropriate or a parallel connected system; For the case in which thel tubes increase in length by equal increments a comparatively simple formula for the resultant impedance results. If n denotes the combining the impedances of the individual im number of tubes, Z the length of the shortest tube, and AZ the increment of length, andif it beassumed' that the tubes are all open ended, the impedance of the combination is given by the equation.

Each of the within the brackets may be expanded intoan infinite series,of which only the first two terms in each case are of importance. Neglecting the unimportant terms and summing up those retained, the following approximate formula is found:

Equation 6 indicates that the impedance of the combination has an average value equal to of the characteristic impedance of each tube. The second term represents the oscillations in the value of the impedance as the frequency-varies. The validity of Equation 6 as an expression for the impedance depends u on the structure being such that the rejection of the higher terms' in the expansion of Equation 5 1s justified. Mathematically the justification requires that the quantity 26m should be small compared wlth n for the lowest frequency' at which the device is to be used. In the structure, since it-is desired to keep the len h of los l the device small, this condition is ac ieved the value 1.6 is small enough to justify ignoring the higher terms.

The variation of the lmpedance correspending to the variation of the second term of `Equation 6 is more readily estimated from a simpler form of the equation obtained by standard trigonometrical transiso - ulus value.

i, ,reimmsmh Pfau 7) y sinh PAZ in which Zn denotes the length of `the longest tube of the group. The second term withinv the brackets is a complex quantity, since P is complex, but in estimating its importance it is sufiicient to determine its mod- Substituting the value a-l-y' for P, and simplifying the expression, the lValue ofmthe modulus is found to be enh wreef@ sinh 21Al+ sin 2AZ The above formula is convenient as a guide in the design of acoustic resistances in accordance with the invention.` The numerical value diminishes very rapidly with frequency, consequently it is necessary to con sider its effect only at the lowest frequency at which the device will be used. At this frequency the value should not exceed the limit of error prescribed by the operating conditions. For the design of acoustic resistances in which the medium is airat nor mal atmospheric temperature and pressure, the following numerical values of the basic coeflicients, expressed in C. G. S. units, may be used:

' gie-a (I+In) The value of a: in Equations 1 and 2 corresponding to these coeliicients is given by d 1:20am).

A convenient design rule is that the length of the shortest tube should be at least equal reaches a constant value and it is therefore desirable to use as large a number of tubes as possible. Considerations ofthe desired resistance value and of the permissible minimum diameter of the tubes, however. place a limit on the number of tubes that may be used.

In the device illustrated in Fig. l the tubular elements combined in pairs each pair comprising one open and one closed tube.

The impedance of the combination is readil found from Equations 3 and 4 to be as fo lows: l -i thPL't hPL Za--Zk C0 'r'. 8.11

ze i.; mnh zPL, (e)

in the manner described, has a normal impedance equal to bz-1 and in uniformity is equivalent to a combination of n tubes of the double length. By doubling the effective length of each element in this manner, a greater degree of uniformity is obtained, or, alternatively, the overall length of the assemlblylffmay be reduced to approximately one ia l.

' If circular tubes are used the interstices Ybetween the tubes constitute an additional series of paths which contribute a resistance in shunt to vthe resistance of the main paths. The amount of the correction, due to the shunt resistance may 'be estimated roughly by the foregoing formulae, or if desired the interstices may be filled up; Since the interstices are very small the parallel impedance due to them is large and their effect on the total resistance is small.

One method of eliminating the interstices is shown in Fig. 4 which shows an end view of an assembly in which the tubes are of hexagonal cross section. Tubes of this form stack up without leaving any air spaces between them. and consequently no correction is required. The assembly of Fig 4 comprises, like that of Fig. l, 37 tubes which are arranged in 18 paired elementsof the t of Fig. 3, together with a single open tu in the center. This center tube may either form part of the resistance proper or it may be used as a gauge tube in connection with an indicatingr device such as a telephone receiver for measuring or indicating the pressure variations at the input end of the resistance.

The normal value of the resistance is substantially equal to the characteristic impedance ot' a 'single tube, Whose cross sectional area is equal to the sum of the areas of the component tubes. One of the important uses of the resistance device is to provide the proper termination or damping for an accustic system, but. if the area of the conduit of the acoustic system 1s smaller than the effective area of the device, thc proper 'terminatransforming means is the device to a system of larger cross secr q tion will not be provided unless some transforming means is introduced vto effect the matching of the impedances. The necessary rovided by the exponentially tapered tu e 3. As is well known, the characteristic acoustic impedance of an exponentially tapered sound conduit at any cross section is inversely pro ortional to the area at that cross section, an is constant and resist-ive at all frequencies above a certain critical frequency determined by the rate of taper. The tapered tube connection brings about the desired impedance matching by transforming the resistance of the device in the inverse ratio of its end areas. To adapt tional area, an expanding tapered tube may obviously be used. By making the tapered tube of a number of detachable sections in the manner shown in Fi 1, the device mayv be adapted to a variety o systems, or may be used under other conditions as a variable resistance.

The eiect of a de arture from the uniform law of variation o the length of the tubes is to produce a superimposed variation on the normal value of the resistance. For example, if all of the tubes were of the same length the superimposed variation would be periodic with respect to frequency, the frequency interval between successive maxima corresponding to the intervals between the successive tube resonances, which in this case occur at the same frequencies in all tubes. If

a the tube lengths vary progressively by some regular law other than the arithmetic proression, a similar periodic variation will result, but the amount of the variation will be less than in the extreme case mentioned above. For certain purposes a non-uniform resistance characteristic may be desirable, and, within limits, may be secured by gradingr the lengths of the tubes in diierent maners.

In Fig` the use of the invention in connection with an acoustic link in a telephone system is illustrated. The acoustic link comrises an acoustic wave filter 10, of the multiband-pass type described in the co-pending application of W'. P. Mason, Seriall No. 201,525 filed June 25, 1927. The main conduit 11 of the filter is connected to resistance devices 12 and 13 by means of the tapered tubes 14 and 15. At the ends of the conduit 11 short side branch tubes of small diameter connect to telephone receivers 16 and 17 in which the telephone lines 18 and 19 terminate. The telephone receivers serve to convert the electrical waves into acoustic pressure variations and also to recouvert the acoustic Waves, after transmission through the filter, into electrical oscillations. Telephone receivers o the electro-magnetic type are capable of translating the Wave energy in both directions and permit two-way trans- .filter are thereby mission through the systems. If transmission in one direction only is desired one of the receivers may be replaced by a microphone. Since the telephone instruments are essentially of high mechanical impedance, they are not adapted to provide, by themselves, the proper termination for the filter. This however, is provided by the resistance devices and the selectiveproperties of the properly develo d. An acoustic link of t e type described a ve may be used for eliminating superimposed noise currents from a telephone circuit. The multi-bandass filter can be so designed that the ban s are ver closely spaced in the `freuency scale, an are separated by narrow bands of very great attenuation spaced at harmonic intervals. The attenuatin ranges ma be so located that they suppress t e noise ma g harmonics of stray currents, induced, for example, by power transmission lines. At the same time the narrowness of the attenuation bands prevents the loss of important speech frequencies. v

The resistance elements ma also be used for terminating other t es o acoustic linksA in telephone systems. stead of the wave filter 10 in the system of Fi 5, the acoustic link may consist of a simp e uniform tube, its purpose being to eiect a dela in the transmission of the speech waves. 'yrhe uniformity of delay, that is characteristic of an ininitely extended uniform tube, is realized in a finite tube only when wave reflection at the ends is eliminated.

The devices of the invention are not restricted to the use described above, but may be used under many conditions where acoustic resistance is desired, or where the damping of the energy of acoustic oscillations 1s required. It is to be observed, moreover, that the principles of the invention are applicable not only to acoustic devices but to wave transmission lines and combinations thereof in general, whether the medium be gaseous, solid, or the conduction of an electrical transmission line. Accordingly the scope of the invention is not to be limited to the articular devices described but only as de ned by the appended claims.

What is claimed is z 1. An acoustic impedance device Icomprising a plurality of tubular elements of graded lengths constituting acoustic wave paths, and means for impressing acoustic wave pressure upon said aths simultaneousl the crosssections an the number of sai tubular elements being so proportioned with respect to a predetermined resistance that said device has an impedance substantially equal to said predetermined resistance over a wide frequency range which extends down to a very low frequency.

2. An acoustic impedance device comprising a plurality of tubular elements of lengths lliv graded in uniform steps emanating cousue paths, and means for impressing acous- Wave tic wave ressure upon said paths simultaueously, t e ratio of inner surface area to vcross-sectional area of each element being large, whereby damped. u

3. An acoustic im edance device according to claim 1 in which t e tubular elements comrise pairs of equal tubes, one of each pair ing closed at one 'end land the other open at both ends.

4. An acoustic impedance device comprising a plurality oftubular elements of prosound waves are substantially 'gresslvely increasing lengths constituting acoustic wave paths, said paths being joined together at one end in a common mouth opening, and an air chamber in front of said `mouth opening lwhereby acoustic wave pres-l fsure may be applied to said paths, the lengths of said elements being suiiicient to substan-v tially damp sound waves therein.

i 5. An acoustlc unpedance devlce comprising a plurality of tubular elements of progressively increasing lengths constituting acoustic wave paths, said tubular elements being stacked parallel to each other to form a close packed assembly of minimum crossvsectional periphery, and being lconnected at one `end to a common air chamber whereby acoustic wave pressure may be applied to all of said paths simultaneously, the viscosity of said paths being substantial whereby sound waves are damped therein.

6. An acoustic impedance device in accordance with claim 5 in which the tubular elements comprise tubes of hexagonal cross-section and are stacked to ether in honeycomb fashion whereby interstices between the tubes yare eliminated.

7. An acoustic impedance device comprising a plurality of tubular elements of progressively increasing` lengths constituting' acoustic wave paths,

ormly, the cross-sections of said elements bemultaneously, and

ing small enough in comparison with their iengths to produce a substantial degree of damping.

8. An acoustic im @dance device in accordance with claim i) in 1which the tapered connecting tube comprises a plurality of detachable sections of progressively increasing diameters.

9. An acoustic impedance device comprisa plurality of ktubular elements of pro gressively increasing lengths constituting acoustic wave paths, means forl impressing acoustic wavepressure upon said paths simeans for varying the acoustic impedance presented by'said paths to the impressed. wave pressure whereby ing a parallel connected system of multiple 4resonant acoustic elements which are so pro portioned with respect to each other that the resonances occur at progressively increasing frequencies, and that the frequency intervals between the successive resonances of the system are small compared with the intervals between the resonances of'each element, each of said elements including an air conduit of such small cross-section that the air vibration at resonance frequencies is substantially damped by viscosity.

11. An acoustic device in accordance with claimv 10 in which each element includes an air conduit the diameter of which is of the order of 0.4 cm.

l2.l An acoustic wave impedance ydevice comprising a connected system of linear ele progressively increasing lengths,A

ments of constituting wave transmission channels in which energy storage and ener dissipation properties are distributed uni the length, said elements being connected at one end to a common Wave input means Wave ener is impressed upon all of the transmission c annels simultaneously, and being terminated at the other ends to produce full wave reflection, the cross-section of each element being small enough in comparison with its length to produce a substantial degree of damping due to viscosity.

13. A wave impedance device comprising a connected system of ylinear elements of progressively increasing lengths, constituting Wave transmission channels in which energy Stora e and energy dissipation properties are distri uted uniformly along the length, said elements being connected at one end to a common input means whereby wave energy is impressed upon all of the transmission channels, each of said elements roviding a pair of equal transmission charme s, one channel of the pair being closed at the end remote from the common junction whereby wave motion is stopped at said closed end, and the other channel being from the common junction whereby there obta'iis freedom of wave motion at said open en In witness whereof, I hereunto subscribe my name this 21st day of September, A. D.

WARREN P. MASON.

ormly along open at the end remote A 

